Your mortgage has $28$ years$$ left, and has an APR of $7\mathrm{.}549\%$ with monthly payments of $$$$1$ comma $486\mathrm{.}81.$

a$.$ What is the outstanding$$ balance?$$

b$.$ Suppose you cannot make the mortgage payment and you are in danger of losing your house to foreclosure. The bank has offered to renegotiate your loan. The bank expects to get $$$$155$ comma $000$ for the house if it forecloses. They will lower your payment as long as they will receive at least this amount$($in present value$$ terms$).$ If current $28-$year mortgage interest rates have dropped to $4\mathrm{.}907\%($APR$),$ what is the lowest monthly payment you could make for the remaining life of your loan that would be attractive to the$$ bank?